The area of the parallelogram spanned by the given vectors is equal to the magnitude of their cross product.
(i + j + k) × (-2i + 3j + k)
= -2 (i × i) - 2 (j × i) - 2 (k × i)
… + 3 (i × j) + 3 (j × j) + 3 (k × j)
… + (i × k) + (j × k) + (k × k)
= - 2 (j × i) - 2 (k × i) + 3 (i × j) + 3 (k × j) + (i × k) + (j × k)
= 2 (i × j) - 2 (k × i) + 3 (i × j) - 3 (j × k) - (k × i) + (j × k)
= 5 (i × j) - 3 (k × i) - 2 (j × k)
= 5 k - 3 j - 2 i
Then the area of the parallelogram is
||-2 i - 3 j + 5 k|| = √((-2)² + (-3)² + 5²) = √38
Answer:
The answer is i (i^9)
Step-by-step explanation:
-10*-4=40, -10+-4=-14 to solve this all that I did was looked for 2 numbers that follow the rules of this equation, and remembering the rules of 2 negative numbers when multiplied I found -4 and -10 because a negative times a negative=a positive. Then when adding to negatives together it becomes even more of a negative number.
Enjoy!=) Hope that this made sense and helped!=)
Answer:
The graph of the line in the attached figure
Step-by-step explanation:
we have
This is the equation of a line into point slope form
The slope is
The line pass through the point (-6,-7)
To graph the line find the y-intercept
Remember that
The y-intercept of the line is the value of y when the value of x is equal to zero
so
For x=0
The y-intercept is the point (0,-3)
with the point (-6,-7) and (0,-3) plot the line
see the attached figure
Answer:
140 minutes
Step-by-step explanation:
The first thing you need to do is figure out how long it takes for Andre to plant 1 seedling. If it takes 30 minutes to plant 3, and they all take the same amount of time, you can divide 30 by 3.
30 total minutes ÷ 3 seedlings = 10 minutes each, so it takes 10 minutes to plant 1 seedling.
Now you need to find how much time it will take to plant 14. To do this multiply 14 by the number of minutes it takes to plant 1 seedling (10 minutes). 14 seedlings × 10 minutes each = 140 minutes total.